core

### Math Process of the Default (I,J,K, T) RMEAS Mode

The Default (I,J,K T) RMEAS mode controls I, J, K, T, and therefore works well with RMEAS features such as planes.

Using the numerical values taken from the example features in the table below, follow these steps to understand how RMEAS/DEFAULT (I,J,K, T) functions when the RMEAS feature is "plane reducible".

A "reducible" feature is a feature that also contains information to be used as another feature. For example, a circle feature is point reducible because a point feature can be automatically extracted from the circle's centroid. It is also line reducible because a line can be drawn along the vector and through the centroid. It is plane reducible because a plane can be drawn intersecting all of the circle's hits.

1. Create a coordinate system (roto-translation matrix) given the nominal RMEAS feature XYZ IJK and the intersection vector between the nominal and the actual RMEAS feature.

2. Move the nominal Auto Feature XYZ and IJK into the RMEAS coordinate system.

3. Zero-out the T value and rotate the nominal Auto Feature XYZ on the plane of the actual RMEAS feature.

4. Offset the transformed Auto Feature XYZ back to the original T offset plus the distance between the actual and the nominal RMEAS feature.

5. Move the transformed Auto Feature XYZ and IJK back into the PART coordinate system.

6. Use the new nominal XYZ and IJK to measure the Auto Feature.

Example Feature | XYZ | IJK
Nominal RMEAS Feature | 0, 0, 2 | 0, 0, 1
Actual RMEAS Feature | -1, 0, 1 | -0.7071, 0, 0.7071
Nominal Auto Feature | 2, 1, 0 | 0.7071, 0, 0.7071
New Nominal Auto Feature | 1.4142, 1, 0.4142 | 0, 0, 1

Example with Translation only | XYZ | IJK
Nominal RMEAS Feature | 124, 50, 0 | 0, 0, 1
Actual RMEAS Feature | 123, 50, -1 | 0, 0, 1
Nominal Auto Feature | 93.5, 19.5, 0 | 0, 0, 1
New Nominal Auto Feature | 93.5, 19.5, -1 | 0, 0, 1